On weak sharp solutions in ( ρ , b , d ) $(\rho , \mathbf{b}, \mathbf{d})$ -variational inequalities

Abstract

Abstract In this paper, weak sharp solutions are investigated for a variational-type inequality governed by ( ρ , b , d ) $(\rho , \mathbf{b}, \mathbf{d})$ -convex path-independent curvilinear integral functional. Moreover, an equivalence between the minimum principle sufficiency property and the weak sharpness property of the solution set associated with the considered variational-type inequality is established.

Keywords

• Weak sharp solutions
• Variational-type inequality
• ( ρ , b , d ) $(\rho , \mathbf{b}, \mathbf{d})$ -convex path-independent curvilinear integral functional